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Differentiability of the generalized solution of a non-linear wave equation. (English) Zbl 0133.35801

Der Verf. behandelt das charakteristische Anfangswertproblem für die nichtlineare Wellengleichung \[ \partial^2u/\partial x_1^2 - \partial^2u/\partial x_2^2 - \partial^2u/\partial x_3^2 = f(x_1, x_2, x_3; u) \] mit verschwindenden Anfangsbedingungen und beweist unter diesen Voraussetzungen die Existenz einer zweimal stetig differenzierbaren Lösung. Anschließend werden einige Differenzierbarkeitseigenschaften der Lösungen diskutiert.
Reviewer: H. Niemeyer

MSC:

35L70 Second-order nonlinear hyperbolic equations
35D99 Generalized solutions to partial differential equations
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References:

[1] S. Aizawa: On the characteristic initial value problem for non-linear wave equations in two space variables, Funkcialaj Ekvacioj, 3, 115-146 (1961). · Zbl 0133.35704
[2] M. Riesz: L’integrale de Riemann-Liouville et le probleme de Cauchy, Acta Math., 81, 1-223 (1949). · Zbl 0033.27601
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